Solving Polynomial Equation Systems II
A complete survey of Gröbner bases and their applications, this book will be essential for all workers in commutative algebra, computational algebra and algebraic geometry. The second volume of the treatise focuses on Buchberger theory and its application to the algorithmic view of commutative algebra. In distinction to other works, the presentation is based on the intrinsic linear algebra structure of Gröbner bases, making this a state-of-the-art reference on issues of implementation.
- Elementary introduction to Groebner bases and Buchberger's Algorithm which also discusses the state-of-the-art of the best implementations
- Survey of last twenty years work on applying Groebner technology to commutative algebra
- Unique in stressing modern framework for computational work and solution methods
Reviews & endorsements
"The material contained in the book is remarkably wide-ranging and includes the most recent developments in the field. The book is ... a fundamental reference for anyone from undergraduate students to researchers interested in (computational aspects of) algebra."
Mathematical Reviews
"I have to admit that I fell in love with this book at first sight; for it is not just extremely well organized, it is also written in a style that is a joy to read... To sum up, this is a wonderful book, beautifully written and produced, that should be in every mathematical library. Actually, if you are a serious user of Gröbner bases you will probably wish to have your own copy of the book, which, I bet will soon be very well thumbed."
S.C. Coutinho, SIGACT News
Product details
June 2005Hardback
9780521811569
784 pages
242 × 165 × 42 mm
1.261kg
Available
Table of Contents
- Preface
- Part III. Gauss, Euclid, Buchberger - Elementary Gröbner Bases:
- 20. Hilbert
- 21. Gauss
- 22. Buchberger
- 23. Macaulay I
- 24. Gröbner I
- 25. Gebauer and Traverso
- 26. Spear
- Part IV. Duality:
- 27. Noether
- 28. Möller I
- 29. Lazard
- 30. Macaulay II
- 31. Gröbner II
- 32. Gröbner III
- 33. Möller II
- Part IV. Beyond Dimension Zero:
- 34. Gröbner IV
- 35. Gianni Trager Zacharias
- 36. Macaulay III
- 37. Galligo
- 38. Giusti
- Bibliography
- Index.
